Abstract

In this study, octonions with eight dimensions and their algebra, which are both noncommutative and nonassociative, are presented. Moreover, the general properties of complex octonions with 16 dimensions and the products of basis are defined by using Cayley–Dickson multiplication rules. Maxwell's equations are taken into consideration when it comes to bi-isotropic media in which the electric and magnetic fields are coupled by means of bi-isotropic constitutive relations. The Drude–Born–Fedorov constitutive relations defined with the complex representations of electric and magnetic fields are used for all calculations. In the next stage, the complex octonionic differential operator is introduced and the octonionic field and source equations are defined for bi-isotropic media. As a result, Maxwell's equations for bi-isotropic media, which are fundamental features that serve as the groundwork for electromagnetism, all of them as being unique, more compact, and a convenient form with magnetic monopole.